Gravitation and cosmology with York time

TL;DR

This thesis explores using York time to address the problem of time in quantum gravity, developing Hamiltonian-reduced cosmological models, perturbation theory, and novel quantisation methods, aiming to advance understanding of quantum cosmology.

Contribution

It introduces York-time Hamiltonian reduction, perturbation theory, and a wavefunction-free quantisation approach for cosmological models in quantum gravity.

Findings

Successful Hamiltonian reduction with York time

Development of perturbation theory around homogeneous backgrounds

Proposal of a trajectory-based quantisation method

Abstract

[Shortened abstract:] In this thesis we investigate a solution to the `problem of time' in canonical quantum gravity by splitting spacetime into surfaces of constant mean curvature parameterised by York time. We argue that there are reasons to consider York time a viable candidate for a physically meaningful notion of time. We investigate a number York-time Hamiltonian-reduced cosmological models and explore some technical aspects, such as the non-canonical Poisson structure. We develop York-time Hamiltonian-reduced cosmological perturbation theory by solving the Hamiltonian constraint perturbatively around a homogeneous background for the physical (non-vanishing) Hamiltonian that is the momentum conjugate to the York time parameter. We proceed to canonically quantise the cosmological models and the perturbation theory and discuss a number of conceptual and technical points, such as volume eigenfunctions and the absence of a momentum representation due to the non-standard commutator structure. We propose an alternative, wavefunction-free method of quantisation based on an ensemble of trajectories and a dynamical configuration-space geometry and discuss its application to gravity. We conclude by placing the York-time theories explored in this thesis in the wider context of a search for a satisfactory theory of quantum gravity.